Our familiarity with the larger domestic animals tends, I think, to mislead us: we see no great destruction falling on them, but we do not keep in mind that thousands are annually slaughtered for food, and that in a state of nature an equal number would have somehow to be disposed of.
From an animal welfare point of view, the question is which is better? The method of "disposal" of man, or of nature? I tend to vote man, as the animals slaughtered for food are well-fed, generally healthy, and the actual death is quick. The animals "disposed of" by nature die of starvation and live with fear, illness and injury. A large domestic animal like cattle, horses, etc, if victims of predation are unlikely to die as quickly once attacked as they would in a modern slaughterhouse.
If that is indeed an accurate statement of your position, then we are far enough apart in this discussion that we will never reach common ground and further debate is a waste of both of our times.
And I do think that it's valid to make a comparison to humans to see if such an argument would hold true if its our own species.